Joe,
While in inverter mode, inverter/chargers can still get toasty. I'm not sure why the internal fan only runs in charger mode. Here's what the Trace SW model manual states:
"As an inverter, overheating can be caused by attempting to operate too large of a load for too long, a failure of the inverter cooling fans, or that the air flow into or out of the inverter is blocked."
Most, if not all, inverter/chargers used by converters will raise an alarm if they get too hot. If the fan is inoperative an overheat alarm will likely be experienced.